Grade 5 Numerical Expressions and Patterns

5.OA.2

About the Math

Full Standard

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Learning Targets (I can)

Write an expression to represent a situation (i.e. 7 more than 8 is expressed as 8 + 7; 7 times a number is expressed as 7 x n)
Analyze expressions by interpreting the relationships among the numbers without evaluating them (i.e. 3 x (750 + 250) is three times as large as 1000.

About the Math

Write an expression to represent a situation (i.e. 7 more than 8 is expressed as 8 + 7; 7 times a number is expressed as 7 x n)

An expression names a number. An equation describes a relationship between two expressions. A variable is a quantity that can change or vary. Variables are often represented with a letter such as, x, n. Any variable can represent any value. When you evaluate an expression, you substitute a number for every variable in the expression. Students need to write expressions that describe word problems. Use numbers when you know what they are and use variables when you don't know the numbers. Often, expressions and other computations can be performed mentally or conjectures can be made about computations or comparisons without precise calculations.

Expressions
Operation	Word Phrase	Algebraic Expression
Addition	A number plus 8 Sum of a number and 8 8 more than a number A number increased by 8	X + 8
Subtraction	A number minus 5 The difference between a number and 5 5 less than a number A number decreased by 5	X - 5
Multiplication	7 times a number A number multiplied by 7 The product of 7 and a number	7 x n 7 , n 7n
Division	A number divided by 9 The quotient of a number and 9	X 9 x ÷ 9

Analyze expressions by interpreting the relationships among the numbers without evaluating them (i.e. 3 x (750 + 250) is three times as large as 1000.

Reasoning about expressions is helpful for evaluating them and making sense of the results. Properties, such as the Distributive Property, can be applied to expressions. Students should also reason or estimate the results of an expression as shown in the learning target. Another example might be that 5(33 - 10) is more than 125 because 5 x 25 is 125.

Essential vocabulary for this standard includes parenthesis, expression, evaluate, and bracket.

Progression of Standard within Grade 5

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1	Quarter 2	Quarter 3	Quarter 4
			Revisit if needed. Write an expression to represent a situation (i.e. 7 more than 8 is expressed as 8 + 7). Analyze expressions by interpreting the relationships among the numbers without evaluating them (i.e. 3 x (750 + 250) is three times as large as 1000.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map. Information is not the complete standard.

Progression Across Grades
Grade	Grade 6
This concept is not taught prior to Grade 5.	Write, read, and evaluate expressions in which letters stand for numbers (6.EE.2) Apply properties of operations to equivalent expressions (6.EE.3) Identify equivalent expressions (6.EE.4) GCM and LCF (6.NS.4)

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

Jackie has 34 marbles and Natalie has 123 marbles. Sarah has four times the amount of marbles as Jackie and Natalie combined. Write the number sentence that shows the number of marbles that Sarah has.
Do you need to do the calculations to know which answer is larger? 6 x (184 + 948) OR (948 + 184) x 3? How much larger will the answer be?
What is a way to write an expression that is five times as much as 96 ÷ 3?
How are the expressions 8 - a and a - 8 different? Explain your thinking.
Write this statement as expression: “Twenty-three less than the sum of forty-nine and thirty-seven.”
Write an expression for twice a number, decreased by twenty-nine, is seven.
How would you write the following expression in words? 32 = 2x + 7. Write a story problem that would go along with this expression.

SLIDE-BASED TASKS

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first (often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.

Module 12 • Expressions, Coordinate Grids, and Geometric Figures

Write and Interpret Simple Expressions:

Additional Tasks

These links provide instructional ideas connected to this standard.

Mascot Suitcase - obverse

Seeing is Believing (Illustrative Mathematics)
Comparing Products (Illustrative Mathematics)
Words to Expressions 1 (Illustrative Mathematics)
Video Game Scores (Illustrative Mathematics)
Hogwarts House Cup (Georgia Department of Education, pgs 27-31)
Hogwarts House Cup Part 2 (Georgia Department of Education, pgs 32-37)
Expression Puzzle (Georgia Department of Education, pgs. 48-54 )
3-Act Task: The Beanbag Dartboard (Georgia Department of Education, pgs. 38-47)
Growing Staircases (Inside Mathematics Lesson)
Perfect Pair (Inside Mathematics)
Tri-Triangles (Inside Mathematics)
Family Vacation Lesson Plan (Utah Core Academy Lesson)
Family Vacation Student Worksheet
Family Vacation Student Map
Family Vacation Mileage Chart
Family Vacation Reference Sheet
Baseball Game Worksheet (Utah Core Academy Lesson)
Candy Shop (Utah Core Academy Lesson)

Tasks From Print Resources

These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.

Print Resources
Book Title	Grade	Pages
Teaching Student-Centered Mathematics	6-8	What Do You Know About the Shapes?, Activity 12.2, Page 227 Tilt or Balance, Activity 12.3, Page 228 Balls, Balls, Balls, Activity 12.8, Page 233 Number Tricks, Activity 12.9, Page 235
Teaching Student-Centered Mathematics	3-5	What's True for All Numbers, Activity 10.12, Page 308 Special Quantities, Activity 10.13, Page 309 Names for Numbers, Activity 10.14, Page 310 Tilt or Balance, Activity 10.15, Page 311 Adjust a Balance, Activity 10.16, Page 312
Hands-On Standards	5-6	108-109 "Expressions with a Variable" 110-111 "Equations with a Variable" 112-113 "Addition and Subtraction Equations" 114-115 "Multiplication and Division Equations"
Brain-Compatible Activities for Mathematics	4-5	121-123 "Weigh to Go" 2-5 "The Mystery of the Mixed-Up Party Lists"
Math In Practice Teaching Fifth-Grade Math	5	Module 2

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

Algebra Match Up (HCPSS-adapted print resource)

INDEPENDENT PRACTICE/HOMEWORK/ASSESSMENT

These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

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Assessment

Learning Targets

Write an expression to represent a situation (i.e. 7 more than 8 is expressed as 8 + 7).
Analyze expressions by interpreting the relationships among the numbers without evaluating them (i.e. 3 x (750 + 250) is three times as large as 1000.

Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.

Rubric for Tasks (pdf)

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